Here is my take, since I owned all three.
Gnex was unusable. Loved the phone, but signal was horrible for calls and Internet, battery was horrible, and I had to get rid of it for those reasons. Very frustrating.
On to the Maxx. Amazing. This phone was absolutely perfect. Everything worked flawlessly. Signal was amazing, battery was amazing. Bluetooth worked better than any other phone I had. What was I missing? I didn't want to get stuck with a phone for next couple of years that has yesterday's processor, and a non HD screen. I use my phone for everything. I gave the phone to my wife, and very skeptical bought the S3. I would have held out for the Maxx HD, figuring that would be my perfect phone considering how much I love the Maxx, but when I found out the phone was shipping with only 1g of ram and ICS I decided to take the plunge and buy the S3.
First couple of weeks I was very impressed with battery life, screen was amazing, and phone was smooth as butter. Does the battery last as long as the Maxx? No. But it gets me through the day with 3 hours of screen time, and charges faster than any phone I've ever had. If you ever run low just slap it on the charger for 20 minutes. No trouble at all. Problems came when I discovered bluetooth issues while syncing to my car. Now the experience is beyond ruined since I had a phone that worked perfectly and traded it in for the bells and whistles. After dealing with this for a while I was starting to regret my decision since it was an important feature for me. Then comes the update. Although everyone is saying it didn't do much, they are wrong. It fixed the issue. Works flawless now, syncing even better than the Maxx, which I thought was perfect as is. Now I have a phone with the best screen out in my opinion, excellent battery life, great camera, and virtually future proof for the next two years with an extremely fast processor and 2G of ram. Not to mention all the latest and greatest technology, and proven update support along with a great developer community. I couldn't be happier with this phone.
Hope this mini review based on my experience helps anyone deciding between these phones.